Search results for "Chow motive"

showing 2 items of 2 documents

Motives of quadric bundles and relative intermediate jacobians of K3-Fano pairs

2015

This thesis consists of two parts. In the first part we study the Chow motive of a quadric bundle of odd relative dimension over a surface. We show that this motive admits a decomposition which involves the Prym motive of the double covering of the discriminant curve.In the second part, we consider Lagrangian fibrations, obtained as relative intermediate Jacobians of families of Fano threefolds containing a fixed K3 surface, and the existence of a symplectic compactification. In a particular case, we study a partial compactification using calculations with the software system Macaulay2.

Quadric bundleMotif de ChowIntermediate Jacobian[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Variété symplectique irréductibleLagrangian fibrationChow motiveFibration LagrangienneJacobienne intermédiaireIrreducible symplectic varietyPaire K3-FanoFibré en quadriquesK3-Fano pair
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On some aspects of Borel-Moore homology in motivic homotopy : weight and Quillen’s G-theory

2016

The theme of this thesis is different aspects of Borel-Moore theory in the world of motives. Classically, over the field of complex numbers, Borel-Moore homology, also called “homology with compact support”, has some properties quite different from singular homology. In this thesis we study some generalizations and applications of this theory in triangulated categories of motives.The thesis is composed of two parts. In the first part we define Borel-Moore motivic homology in the triangulated categories of mixed motives defined by Cisinski and Déglise and study its various functorial properties, especially a functoriality similar to the refined Gysin morphism defined by Fulton. These results…

Quillen’s K-theory and G-theoryStructure de poidsMixed motives[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Motivic homotopy theoryHomologie de Borel-MooreThéorie de l’homotopie motiviqueMotifs de ChowChow motives[MATH.MATH-KT] Mathematics [math]/K-Theory and Homology [math.KT]G-théorieFormalisme des six foncteursWeight structureSix functors formalismMotifs mixtesRefined Gysin morphismBorel-Moore homologyMorphisme de Gysin raffinéK-théorie de Quillen
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